It is shown that every n-homogeneous continuous polynomial on a Banach space E which is weakly continuous on the unit ball of E is weakly uniformly continuous on the unit ball of E. Applications of the result to spaces of polynomials and holomorphic mappings on E are given. © 1983.
Aron, R. M., Hervés, C., & Valdivia, M. (1983). Weakly continuous mappings on Banach spaces. Journal of Functional Analysis, 52(2), 189–204. https://doi.org/10.1016/0022-1236(83)90081-2